In this paper we show that the monotone difference methods with smooth numericalfluxes possess superconvergence property when applied to strictly convex conservation laws with piecewise smooth solutions. More precisely, it is shown that not only the approximation solution converges to the entropy solution, its central difference also converges to the derivative of the entropy solution away from the shocks.
|Number of pages||26|
|Journal||Hokkaido Mathematical Journal|
|Publication status||Published - 2007|
Scopus Subject Areas
- Conservation laws
- Finite difference
- Monotone scheme